We prove that the only relation imposed on the Hodge and Chern numbers of a compact Kähler manifold by the existence of a nowhere zero holomorphic one-form is the vanishing of the Hirzebruch genus. We also treat the analogous problem for nowhere zero closed one-forms on smooth manifolds.

中文翻译：

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Kähler 流形的全纯一型、圆上的纤维化和特征数

我们证明了由无处零全纯一型的存在强加给紧致 Kähler 流形的 Hodge 和 Chern 数的唯一关系是 Hirzebruch 属的消失。我们还处理光滑流形上无处零闭一形式的类似问题。